Triangle L M N is cut by line segment O P. Line segment O P goes from side M L to side M N. The length of O L is 14, the length
of O M is 28, the length of M P is y, and the length of P N is 18.
Which value of y would make O P is parallel to L N?
16
24
32
36
Which value of y would make O P is parallel to L N?
16
24
32
36
2 answers:
Answer:
The value of y that would make O P parallel to L N = 36
Step-by-step explanation:
This is a question on similar triangles. Find attached the diagram obtained from the given information.
Given:
The length of O L = 14
the length of O M = 28
the length of M P = y
the length of P N = 18
Length MN = MP + PN = y + 18
Length ML = MO + OL = 28+14 = 42
For OP to be parallel to LN,
MO/ML = MP/PN
MO/ML = 28/42
MP/PN= y/(y+18)
28/42 = y/(y+18)
42y = 28(y+18)
42y = 28y + 18(28)
42y-28y = 504
14y = 504
y = 504/14 = 36
The value of y that would make O P parallel to L N = 36
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Part 3) <span>Given triangle XYZ as shown at right find YZ rounded to the nearest tenth
we know that
</span><span>the sum of the internal angles of a triangle add up to 180 degrees
</span>so
m∠X=180-[55+29]----> 96°
applying the law of sines
YZ/sin X=35/sin 55°------> YZ=35*sin 96/sin 55-----> YZ=42.49
YZ=42.5 units
the answer Part 3) is
YZ=42.5 units
Part 4)
we know that
OQ/NQ=PR/NR
NQ=4X+(2X+2)---> 6X+2
OQ=2X+2
PR=15
NR=24+15----> 39
(2X+2)/(6X+2)=15/39
39*(2X+2)=15*(6X+2)
78X+78=90X+30
90X-78X=78-30
12X=48
X=4
The answer part 4) is
x=4
Part 5) A trapezoid is show below. Calculate the measure of angle x. Round to the nearest tenth of a degree
see the picture with letters attached to better understand the problem
we know that
BC=36-28-----> 8 ft
sin x=BC/AC-----> sin x=8/12
x=arc sin(8/12)-------> x=41.81°------> x=41.8°
the answer Part 5) is
x=41.8°
we know that
</span><span>the sum of the internal angles of a triangle add up to 180 degrees
</span>so
m∠X=180-[55+29]----> 96°
applying the law of sines
YZ/sin X=35/sin 55°------> YZ=35*sin 96/sin 55-----> YZ=42.49
YZ=42.5 units
the answer Part 3) is
YZ=42.5 units
Part 4)
we know that
OQ/NQ=PR/NR
NQ=4X+(2X+2)---> 6X+2
OQ=2X+2
PR=15
NR=24+15----> 39
(2X+2)/(6X+2)=15/39
39*(2X+2)=15*(6X+2)
78X+78=90X+30
90X-78X=78-30
12X=48
X=4
The answer part 4) is
x=4
Part 5) A trapezoid is show below. Calculate the measure of angle x. Round to the nearest tenth of a degree
see the picture with letters attached to better understand the problem
we know that
BC=36-28-----> 8 ft
sin x=BC/AC-----> sin x=8/12
x=arc sin(8/12)-------> x=41.81°------> x=41.8°
the answer Part 5) is
x=41.8°